Тысячники (Laminar and Turbulent Boundary Layers)

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Laminar and Turbulent Boundary Layers


A boundary layer may be laminar or turbulent. A laminar boundary layer is one where the flow takes place in layers, i.e., each layer slides past the adjacent layers. This is in contrast to Turbulent Boundary Layers shown in Fig.6.2 where there is an intense agitation.


In a laminar boundary layer any exchange of mass or momentum takes place only between adjacent layers on a microscopic scale which is not visible to the eye. Consequently molecular viscosity is able predict the shear stress associated. Laminar boundary layers are found only when the Reynolds numbers are small. A turbulent boundary layer on the other hand is marked by mixing across several layers of it. The mixing is now on a macroscopic scale. Packets of fluid may be seen moving across. Thus there is an exchange of mass, momentum and energy on a much bigger scale compared to a laminar boundary layer. A turbulent boundary layer forms only at larger Reynolds numbers. The scale of mixing cannot be handled by molecular viscosity alone. Those calculating turbulent flow rely on what is called Turbulence Viscosity or Eddy Viscosity, which has no exact expression. It has to be modelled. Several models have been developed for the purpose.

Separation of Flow

Pressure gradient is an is one of the factors that influences a flow immensely. It is easy to see that the shear stress caused by viscosity has a retarding effect upon the flow. This effect can however be overcome if there is a negative pressure gradient offered to the flow. A negative pressure gradient is termed a Favourable pressure gradient. Such a gradient enables the flow. A positive pressure gradient has the opposite effect and is termed the Adverse Pressure Gradient. Fluid might find it difficult to negotiate an adverse pressure gradient. Sometimes, we say the the fluid has to climb the pressure hill. One of the severe effects of an adverse pressure gradient is to separate the flow. Consider flow past a curved surface as shown in Fig.6.4. The geometry of the surface is such that we have a favourable gradient in pressure to start with and up to a point P. The negative pressure gradient will counteract the retarding effect of the shear stress (which is due to viscosity) in the boundary layer. For the geometry considered we have a an adverse pressure gradient downstream of P.


Now the adverse pressure gradient begins to retard. This effect is felt more strongly in the regions close to the wall where the momentum is lower than in the regions near the free stream. As indicated in the figure, the velocity near the wall reduces and the boundary layer thickens. A continuous retardation of flow brings the wall shear stress at the point S on the wall to zero. From this point onwards the shear stress becomes negative and the flow reverses and a region of recirculating flow develops. We see that the flow no longer follows the contour of the body. We say that the flow has separated. The point S where the shear stress is zero is called the Point of Separation.


Depending on the flow conditions the recirculating flow terminate and the flow may become reattached to the body. A separation bubble is formed. There are a variety of factors that could influence this reattachment. The pressure gradient may be now favourable due to body geometry and other reasons. The other factor is that the flow initially laminar may undergo transition within the bubble and may become turbulent. A turbulent flow has more energy and momentum than a laminar flow. This can kill separation and the flow may reattach. A short bubble may not be of much consequence. On aerofoils sometimes the separation occurs near the leading edge and gives rise to a short bubble. What can be dangerous is the separation occurring more towards the trailing edge and the flow not reattaching. In this situation the separated region merges with the wake and may result in stall of the aerofoil (loss of lift).

Drag

Drag is a force that opposes motion. An aircraft flying has to overcome the drag force upon it, a ball in flight, a sailing ship and an automobile at high speed are some of the other examples. It is clear that viscosity is an agent that causes drag. We have seen that it gives raise to boundary layers on solid surfaces. There is shear stress in boundary layers that do tend to retard the motion of fluid past the solid surface. This is sketched for an aerofoil surface in Fig.6.6. This is termed Skin friction Drag. There is another agent that can cause drag. This is the pressure difference upon the flow.

This could come about due to geometrical effects that induce separation as happens with a cylinder to be discussed later. This is called Pressure Drag or Form Drag, since it is due to the body geometry.


The sum of pressure drag and skin friction drag constitutes Drag about the body or Profile Drag.

The shape of the body determines the relative magnitude of the drag components. A thin body (small t/l ratio) as shown in Fig.6.7 obviously causes less pressure drag. Almost all drag comes from skin friction. A thick body (large t/l ratio) is readily prone for separation and produces considerable pressure drag. Streamlining a body to avoid separation will enable to decrease pressure drag considerably. It is obvious that a bluff body like a cylinder or a sphere or a flat plate placed normal to flow will cause separation and lead to pressure drag which may far more than the skin friction drag. In case of a flat plate placed parallel to flow (Fig.6.8), it is the skin friction drag that dominates. On the other hand, in case of a flat plate placed normal to flow, it is the pressure drag that dominates. In the latter case, the plate behaves like a blunt body and gives raise to separation behind it which contributes to pressure drag.




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